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∫e^x/(e^x+2)dx?
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∫(x²e^x)/(x+2)²dx
=∫(x²+4x+4-4x-8+4)e^x/(x+2)²dx
=∫((x+2)²-4x-8+4)e^x/(x+2)²dx
=∫(x+2)²e^x/(x+2)²dx - 4∫(x+2)e^x/(x+2)²dx + 4∫e^x/(x+2)²dx
=∫e^xdx - 4∫e^x/(x+2)dx + 4∫e^x/(x+2)²dx
=e^x - 4∫1/(x+2)d(e^x) + 4∫e^x/(x+2)²dx
=e^x - 4e^x/(x+2) - 4∫(e^x)/(x+2)² + 4∫e^x/(x+2)²dx
=e^x - 4e^x/(x+2) + C
=∫(x²+4x+4-4x-8+4)e^x/(x+2)²dx
=∫((x+2)²-4x-8+4)e^x/(x+2)²dx
=∫(x+2)²e^x/(x+2)²dx - 4∫(x+2)e^x/(x+2)²dx + 4∫e^x/(x+2)²dx
=∫e^xdx - 4∫e^x/(x+2)dx + 4∫e^x/(x+2)²dx
=e^x - 4∫1/(x+2)d(e^x) + 4∫e^x/(x+2)²dx
=e^x - 4e^x/(x+2) - 4∫(e^x)/(x+2)² + 4∫e^x/(x+2)²dx
=e^x - 4e^x/(x+2) + C
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